Hybrid Peer-to-Peer Media Distribution Systems: a Performance Study

1. Hybrid Peer-to-Peer Media Distribution Systems: a Performance Study Yicheng Tu, Jianzhong Sun and Sunil Prabhakar Department of Computer Sciences, Purdue University Paper published in ACM/SPIE Conference on Multimedia Computing and Networking (MMCN04)

2. Media Distribution • Streaming needed • QoS important • Network bandwidth is the bottleneck • Multicast: CNN.COM • Unicast: online cinema • We concentrate on the latter • Server-based system lacks sufficient capacity • Improve capacity by proxies • Contention Distribution Networks (CDNs)

3. Peer-to-Peer in Media Streaming • CDNs are expensive to build • Investment increases as popularity of content does • Peer-to-Peer(P2P) approach: • The idea: Utilize bandwidth among clients (peers) • Inexpensive • Capacity grows as popularity does • Problems of P2P systems: • Object searching is slow in pure P2P system (e.g. Gnutella) • Limited/heterogeneous contributions from peers • Many-to-one streaming, difficult to synchronize • Duration of peer contribution (Peer failure)

4. Hybrid System = CDN + P2P • Combine the advantages of both CDN and P2P • Increase of bandwidth by a P2P community • Search is done by a centralized directory server • Assume object updating is of reasonable frequency • A small number of seed servers: • Used for streaming • Boot up the system • Complementary bandwidth source in case of failure • System model and failure-resistant streaming protocol proposed by Xu et al. (2002) and Heefeda et al.(2003)

5. This Research • Our Goal: To study the system dynamics of the aforementioned hybrid media streaming system • Our approach: mathematical analysis • Non-trivial, a good model is the key • Previous attempt (Xu et al., 2002) gives no analytical results • Confirm analysis by large-scale simulation

6. System Model • Players: • Directory Server • Servers • Same name: Streaming servers, CDN servers • Peers (clients) • Requesting peer • Supplying peer • Qualified peer • Media objects • Operations • Order of streaming entities: peers > servers

7. (Initial) Assumptions • Only one object in the system and they are of the same streaming length (L) and bitrate(b) * • The server side upload link is always the bottleneck • Peer has infinite storage * • Peer never fails * • Requests are uniformly distributed among the peer population

8. Metrics • System capacity: • total bandwidth of servers + qualified peers • Server-peer transition time (k0) *** • Reject rate

9. Intuitively • System capacity growth analogous to population growth of a single species in a biological system • Servers and supplying peers give birth to requesting peers • Each streaming cycle equals a generation • Exponential growth

10. Mathematically Note α/b is the Capacity Growth Factor, the above can be transformed into

11. In a system with requesting rate λ, the condition for server-peer transition is: We get k0 as: More on Mono-file System

12. What About Multi-file Systems? • Previous framework cannot be applied here directly • Difficult to model the interactions between per-file proliferation • Analysis in a rather “indirect" way • View system as a combination of Findependent subsystems with and • Statistical multiplexing (reality) vs. Sharing Multiplexing (our view) • Then prove the above “view” is close to reality

13. k0 in Multi-file System • Each subsystem follows previous analysis • Still it is hard to get k0 for the whole system • System-level k0 depends on distribution of Nf • Nf is unknown • λf is also unknown, but it doesn’t matter • Lets forget about the real solution to k0 for a while and think about the optimal solution !!

14. Optimizing System-level k0 • An observation: k0 is the maximum of all k0,f • System reaches transition only when all single-file subsystem do • The optimization: Minimize k0 = max {k0,f} (0≤f≤F ) Subject to

15. Optimal Choice of Nf The above optimization has solution: k0 = k0,1 = k0,2 = … = k0,F Putting into the k0,fformula: And for all f, we get: What does this mean? • The optimal choice of Nf is directly related to λf • Surprisingly, the optimal k0can be expressed by the same formula for mono-file system

16. To Make the Story Complete • We proved the system converges to the optimal distribution of server bandwidth (Nf) • We used confidence intervals to analyze how close the system is to the optimal situation • When bNλf/λ> 10, very close ! • What about the assumption of independence among subsystems • We introduce an "independence coefficient”β • βis close to 1 when the pool size M is big • Good thing: M should be and is big in general

17. Effects of Peer Failures • Critical feature of any P2P system, cannot ignore • Relate to the biological model: individuals die • Model failures by assigning a lifespan to each peer, denoted as a random number X • Assume a survival rate γ • For any streaming period k, γ= Pr { X ≥T(k)+ L | X >T(k)} where T(k) is the starting time for period k.

18. Effects of Peer Failures • Generally,γis difficult to get • It changes with age (k) • More specifically, it depends on the age structure • Previous study (Saroiu et al., 2002)shows that peer lifespan follows an exponential distribution • Revisit the survival rate, where s is the average lifespan. • The next steps become easy

19. Effects of Peer Failures • With a universalγvalue, • Everything else is the same • The transition time • Note the Capacity Growth Factor becomesγ(1+α/b)

20. Experimental Results

21. Experiments: Effects of α

22. Effects of λ

23. Effects of Media Number

24. Number of Peers by Storage Use

25. Effects of Peer Failure

26. Conclusions • The hybrid streaming system follows an exponential growth pattern • The Capacity Growth Factor affects system performance more than other factors do • Within some boundary, capacity growth of multi-file and mono-file systems can be described by the same equation • Peer failures have significant effects on system capacity, it could kill the system • Quantitative analysis of complex system is hard, but doable in some cases

27. References • D. Xu, H-K. Chai, C. Rosenburg and S. Kulkarni. Analysis of a Hybrid Architecture for Cost-Effective Streaming Media Distribution. In Proc. of ACM/SPIE MMCN 2003,January 2003. • M. Hefeeda,  A. Habib, B. Botev, D. Xu,  B. Bhargava, PROMISE:  Peer-to-Peer Media Streaming  Using CollectCast. In Proc. of  ACM Multimedia 2003, Berkeley, CA,  November 2003 • S. Saroiu, P. K. Gummadi and S. D. Gribble. A Measurement Study of Peer-to-Peer File Sharing Systems. In Proc. of ACM/SPIE MMCN 2002,January 2002.